Travelling Sales Person Problem

Classical Travelling Sales Person Problem solution using Particle Swarm Optimization and Fuzzy Based Algorithm

Abstract— Travelling Sales Person Problem is one of the classical combinatorial optimization problems that belong to the NP-complete class. It is the problem of finding the optimized path for a given set of cities. The path is drawn in such a way that the salesperson has to visit each city exactly once. This paper provides an efficient method for solving the classical Travelling Sales Person Problem by using Particle Swarm Optimization (PSO) based on fuzzy logic. A particle is represented using a particle encoding/decoding scheme for the Travelling Sales Person Problem (TSPP). The searching ability of the PSO is expanded here by

If the group of animals does not have leaders will find the food by random and follow tone of the members of the group that has the closest position of the food source and find the better solution. Animals which have better solution will inform it to its flocks and others will move accordingly. This process happens repeatedly until the best condition or the food source is discovered.

Travelling Sales Person Problem is the most basic computational problems for finding the optimized route in a network. This paper provides a novel approach to find the optimized solution for the single source and finding the shortest path by applying the fuzzy rules to the Particle Swarm optimization technique. The Travelling Sales Person Problem (TSPP) is one of the important basic computational problems in graph theory, and of greatest importance in communication networks. This TSP problem is concerned with exploring the shortest path from a particular origin to a specific target in a specified network however minimalizing the cost and perhaps taking particular limits into consideration. This problem has many

The fuzzy inference process includes membership functions, logical operations, and If-Then rules. There are two kinds of fuzzy inference systems, Mamdani-type [18] and Sugeno-type [19]. These two types of inference systems differ slightly in the way outputs are established. Mamdani 's fuzzy inference method, which is used in this paper, is the most regularly seen fuzzy methodology. Mamdani 's approach was amongst the first control systems built using fuzzy set theory. Sinking into the trap of local optimum and slow merging are of the most important limitations of the PSO. There have been many schemes proposed to solve the first problem, all of which comprise detecting the local optimum and preventing it. In [20], to avoid from achieving the local optimum, when the velocity of the particle is lower than a specific level, but the fitness is not appropriate, a function is used to give a jolt to the particle and increase its velocity. In [21, 22], a non-linear function for reducing the inertia weight is used to rise the velocity of a particle when the inertia weight is small, but the fitness is undesirable. All these methods prevent the particles to converge to a local optimum and some even speed up the convergence. In this paper, a fuzzy-based method proposed by Noroozi and Meybodi [12] is used to overcome the above-mentioned shortcomings of the PSO. In this method, a